What was already known
The two-copy threshold for NPT Werner states was a longstanding open problem, with earlier reductions to a rank-two partial-trace inequality and partial 4×4 progress. Several near-contemporaneous papers give independent solutions.
AI involvement
Song and Chen credit GPT-5.5 Pro with the initial formulation and proof of Proposition 2; they checked it and supplied the remaining argument.
The model originated a retained central proposition, while the final inequality and Werner consequence also depend on human work.
Importance
Provides a central step in one proof of the two-copy Werner-state threshold.
Limitations
The model did not supply the complete nondistillability proof. Fu, Gao and Park gave a separate solution, and other near-contemporaneous work reached the partial-trace result independently.
Technical verification
The authors explicitly report checking the model-generated Proposition 2 argument in full; this is human proof checking of the assessed AI contribution.
Formal checking
Checked the generated argument in full and presented its proof in Appendix A
- Checker
- Human authors of the partial-trace manuscript
- Scope
- Proposition 2 decomposition of q⁽²⁾₋₁/₂(C) for rank-at-most-two C
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain how the projection decomposition leaves a single obstruction term and how their later lemma controls it.
Correction and publication history
Provides a central step in one proof of the two-copy Werner-state threshold.
Read this published revision